In this paper, we investigate how to scale up kernel methods to take on large-scale problems, on which deep neural networks have been prevailing. To this end, we leverage existing techniques and develop new ones. These techniques include approximating kernel functions with features derived from random projections, parallel training of kernel models with 100 million parameters or more, and new schemes for combining kernel functions as a way of learning representations. We demonstrate how to muster those ideas skillfully to implement large-scale kernel machines for challenging problems in automatic speech recognition. We valid our approaches with extensive empirical studies on real-world speech datasets on the tasks of acoustic modeling. We show that our kernel models are equally competitive as well-engineered deep neural networks (DNNs). In particular, kernel models either attain similar performance to, or surpass their DNNs counterparts. Our work thus avails more tools to machine learning researchers in addressing large-scale learning problems.